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Single-Source Shortest Path Problem in Weighted Disk Graphs

Authors Shinwoo An , Eunjin Oh , Jie Xue

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Disk graphs
  • shortest path problem
  • compressed quadtrees

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Abstract

In this paper, we present efficient algorithms for the single-source shortest path problem in weighted disk graphs. A disk graph is the intersection graph of a family of disks in the plane. Here, the weight of an edge is defined as the Euclidean distance between the centers of the disks corresponding to the endpoints of the edge. Given a family of n disks in the plane whose radii lie in [1,Ψ] and a source disk, we can compute a shortest path tree from a source vertex in the weighted disk graph in O(nlog² n log Ψ) time. Moreover, in the case that the radii of disks are arbitrarily large, we can compute a shortest path tree from a source vertex in the weighted disk graph in O(nlog⁴ n) time. This improves the best-known algorithm running in O(nlog⁶ n) time presented in ESA'23.

Cite As Get BibTex

Shinwoo An, Eunjin Oh, and Jie Xue. Single-Source Shortest Path Problem in Weighted Disk Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.7

Author Details

Shinwoo An
  • Pohang University of Science and Technology, South Korea
Eunjin Oh
  • Pohang University of Science and Technology, South Korea
Jie Xue
  • New York University Shanghai, China

Funding

The work by Ah and Oh was supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.RS-2024-00440239, Sublinear Scalable Algorithms for Large-Scale Data Analysis) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.RS-2024-00358505).

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